Tuning curve of type-0 spontaneous parametric down-conversion

The understanding of the spatiotemporal structure of the spectrum is of importance for all applications where entanglement in energy is the relevant degree of freedom and allows optimizing the spectrum for specific applications. Here, we consider spontaneous parametric down-conversion (SPDC) induced by an undepleted monochromatic pump beam of angular frequency ω_ρ with a transverse field distribution ε_p⁺(q_p), which propagates along the z-axis of a periodically poled potassium titanyl phosphate (PPKTP) crystal. The pump photon (p) is down-converted into the idler (i) and signal (s) photon with frequency ω_; = ω_ρ - ω_s and ω_s, respectively.